{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Normal Distribution\n",
    "\n",
    "- Different displays of normally distributed data\n",
    "- Compare different samples from a normal distribution\n",
    "- Check for normality\n",
    "- Work with the cumulative distribution function (CDF)\n",
    "\n",
    "Author:  Thomas Haslwanter, April-2020"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats as stats\n",
    "\n",
    "# seaborn is a package for the visualization of statistical data\n",
    "import seaborn as sns\n",
    "sns.set(style='ticks')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Different Representations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "''' Different aspects of a normal distribution'''\n",
    "# Generate the data\n",
    "x = np.r_[-10:10:0.1]\n",
    "rv = stats.norm(0,1)   # random variate\n",
    "\n",
    "x2 = np.r_[0:1:0.001]\n",
    "\n",
    "ax = plt.subplot2grid((3,2),(0,0), colspan=2)\n",
    "plt.plot(x,rv.pdf(x))\n",
    "plt.xlim([-10,10])\n",
    "plt.title('Normal Distribution - PDF')\n",
    "\n",
    "plt.subplot(323)\n",
    "plt.plot(x,rv.cdf(x))\n",
    "plt.xlim([-4,4])\n",
    "plt.title('CDF: cumulative distribution fct')\n",
    "\n",
    "plt.subplot(324)\n",
    "plt.plot(x,rv.sf(x))\n",
    "plt.xlim([-4,4])\n",
    "plt.title('SF: survival fct')\n",
    "\n",
    "plt.subplot(325)\n",
    "plt.plot(x2,rv.ppf(x2))\n",
    "plt.title('PPF')\n",
    "\n",
    "plt.subplot(326)\n",
    "plt.plot(x2,rv.isf(x2))\n",
    "plt.title('ISF')\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Shifted distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Shifted Normal Distribution')"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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+ybK+shDNQBKBEDdRfLmKpJQzPDC8Bz5dOzbKPnt4uTF6mC//TT5NqdQViBZAEoEQN7E95QzVBhNTx/o16n6njvWjqtrIjh/lDSJhe5IIhLgBvcHIf/ecZnh/baM3AuvTrRNB/l35zw+nMBhNjbpvIRpKEoEQN/DdwRwulVYRNfqOJtl/1Og7uFhcyZ7D55tk/0LUlyQCIW5ge8oZeni5MrSfxuq6t2J4fy98unZke8qZJtm/EPUliUCI6zh9vpjjZ4sIDendZGMJ2NmpCB3Ri59PXeScrrRJjiFEfUgiEOI6dv54Fgd7O8YO79Gkxxl3V0/s1Sp2SrcTwoYkEQhxjSq9kW9Sz3FPYDfcOzo26bE83JwYMdiHXft/QW8wNumxhLgRSQRCXOPAUR1llQbG3dW0TwO1xt/Vk9JyPQeO6prleEJcy+rANACJiYmsW7cOg8FATEzMDccNXrhwISEhIUydOpWLFy8yc+ZM87LS0lKKioo4ePAg+/bt45lnnsHb2xuAgQMHsnLlykY4HSFu37c/ZePh5sQQv6apJL7WsH4aPNyc+CY1m5FDujXLMYW4mtVEoNPpWL16NVu2bMHR0ZFHHnmEESNG4OfnZ7HO0qVLSUlJISQkBIAuXbqQkJAAgMlkIiYmhtjYWAAyMjKYOXMmc+fObYpzEuKWXa6o+cs8bGTvZhtjWK22Y8wwX/675xQlZdVNXhwlxLWsFg0lJycTEhKCh4cHLi4uhIaGkpSUZLFOYmIi48aNIyws7Lr7+OKLL+jQoQORkZEApKen88MPPxAZGcm8efO4cOFCI5yKELfvx/Tz6A0mxtzZvCPgjR3ui8Go8MPhnGY9rhBQj0SQl5eHRnPlEVmr1aLTWZZlzpo1i+nTp193e6PRyHvvvccLL7xgnufm5sbjjz9OYmIiY8aMMT8pXK2kpITs7GyLT25ubr1PTIhb8e1POfh06Yh/D49mPW7f7p3o4eUqjcuETVgtGjKZTBbvUSuK0qD3qr///nt69+5NQMCVnhuXLVtm/v7oo4/y1ltvUVpaipvblWb8GzZsIC4urt7HEeJ2FZZUkpaVz/Tx/Zqs7cCNqFQqRgV247OvT3CptAoPt4aNgCbE7bD6RODt7U1+fr55Oj8/H61WW+8DfP3110yaNMk8bTKZWLduHUaj5atyarXaYjomJoZdu3ZZfDZu3Fjv4wrRUD8cysGkwJhhzVssVOuewG6YFPgxQ4pKRfOymghGjRpFSkoKhYWFVFRUsHPnTkaPHl3vAxw6dIjg4OArB7Sz46uvvmLHjh0AxMfHExQUhIuLi8V27u7u+Pr6Wnxq3zISoil8ezCbvt06NXoHc/XV28edbl07sidNiodE87KaCLy8vIiNjSU6OprJkycTERFBYGAgs2fPJj093eoBzp07V+cG/sYbb/DRRx8RHh7OF198wfLly2/9DIRoBLkXyzjxyyVGD+tusxhUKhX3BHUjLauAkjIZp0A0n3q1I4iMjDS/8VNr/fr1ddZ7/fXX68w7fPhwnXn+/v588skn9Y1RiCa39+eaFxFGBt7awPSNZVRgNz7blcnejAtMGNHLprGI9kNaFgsB7M3Ipae3G926uto0jju6d8LL00WKh0SzkkQg2r3S8mp+Pn2REYNsXwelUqm4J7AbhzPzuSzDWIpmIolAtHv7j+gwmRRCBtu2WKjWPUHdMBgV9h2RdjOieUgiEO3e3p8v4OnuhJ9v8zYiuxH/Hh509ehASrq8RiqahyQC0a5V6438dCyPuwf5YNdMfQtZo1KpuGuAF4dO5EvX1KJZSCIQ7VpaVgGV1UZCBtu+fuBqdw30orLaSMbJi7YORbQDkghEu/ZjxgU6ONkT6NfV1qFYGOLXFUd7O/bLGAWiGUgiEO2WyaSw7+dc7uyvxcFebX2DZuTsaE+gv4YDR3QoimLrcEQbJ4lAtFtZ2ZcoKq1qEa+NXk/wAC8uXCwjJ/+yrUMRbZwkAtFupR7LQ6WCOwPq34lic7prgBdQ83qrEE1JEoFot346psO/hwedXFtml89aTxd6ebvJWMaiyUkiEO1SaXk1J34p4s4AL1uHclPBA7z4+dRFyir0tg5FtGGSCES7dOh4PiYFhvdvmcVCte4a6I3RpHDwRJ6tQxFtmCQC0S6lHtfh2sEB/56dbR3KTfXv1RnXDg5STyCalCQC0e6YTAo/HctjWIAWdQtpTXwjarUdQ/tpOHQiT14jFU1GEoFod85cKKGotKrFvi10rWEBWgpLqvglt9TWoYg2ql6JIDExkUmTJjFx4sSbjhu8cOFCtmzZYp7eunUr9957L1FRUURFRbF69WoASkpKmDNnDmFhYcyYMcNiTGQhmlrqsZpiljtbeP1ArWH9auKUegLRVKwmAp1Ox+rVq9m0aRPx8fF8+umnZGVl1Vln3rx55nGIa2VkZLBo0SISEhJISEggNjYWgDVr1hAcHMz27duZPn06K1asaMRTEuLmUo/l0bdbJzzdnW0dSr1oOnegh5crB4/LH0yiaVhNBMnJyYSEhODh4YGLiwuhoaEkJSVZrJOYmMi4ceMICwuzmJ+ens7WrVuJjIzkxRdfpLi4GIDdu3ebh76MiIjgu+++Q6+X1+NE0yur0HPsTGGreRqoNayfloyTBVTrpTdS0fisJoK8vDw0Go15WqvVotNZvsEwa9Yspk+fXmdbjUbDU089xZdffomPjw/Lli2rs097e3tcXV0pLCy02LakpITs7GyLT26uDNQhbk/GyQKMJqXV1A/UGhagpdpg4shp6Y1UND6rg9ebTCZUqitvViiKYjF9M2vXrjV/nzVrFhMmTLjueoqiYGdnmZM2bNhAXFxcvY4jRH0dzirA0UFN/94t+7XRaw3u2wV7tYqDx/MZ2q91JTHR8ll9IvD29raozM3Pz0ertf6DWFpayocffmieVhQFtbqmh0etVktBQQEABoOBsrIyPDwsR4eKiYlh165dFp+bVVQLUR9pmfkM7OPZ4nobtcbZyZ6Bfbrw03GpMBaNz2oiGDVqFCkpKRQWFlJRUcHOnTsZPXq01R27uLjwwQcfcPjwYQA+/vhj8xPBmDFjiI+PB2Dbtm0EBwfj4OBgsb27uzu+vr4WH2/vltlLpGgdikorOZtb2uLGHqivof00nLlQQmFJpa1DEW2M1UTg5eVFbGws0dHRTJ48mYiICAIDA5k9ezbp6ek33E6tVrNmzRpeeeUVwsLC+Pnnn1mwYAEA8+fP59ChQ4SHh7Np0yZefvnlxjsjIW4gPavmKTTIX2NlzZZp2K/1GodOyNtDonFZrSMAiIyMNL/lU2v9+vV11nv99dctpoODg9m6dWud9Tw8PHjvvfcaEqcQty0tq4COzvbc0b2TrUO5JX27daKTqyMHT+TxQHAPW4cj2hBpWSzajcOZ+Qy+oytqdev8sbezUxHkpyEtM1+6mxCNqnX+RgjRQLrCcnIvlhPo3zrrB2oF+nelsKSK7DwZtUw0HkkEol1Iy6wpVw/ya531A7Vq6zdqz0eIxiCJQLQLaVkFeLg60dPbzdah3BYvTxe0nTtw+NeKbyEagyQC0eYpikJaVj6Bfl3r3RiypVKpVAT5a0jPqmkhLURjkEQg2rzsvMsUllS1+vqBWoF+Xblcoed0TrGtQxFthCQC0eaZ6wdaafuBawXW1hNkST2BaBySCESbdzirAG3nDnh5utg6lEbh6e5MDy9XDmdKPYFoHJIIRJtmNCmkZxUQ6Kdp9fUDVwvy0/Dz6YvoDSZbhyLaAEkEok07fb6YyxV6gtpI/UCtQH8NVdVGTvxSZOtQRBsgiUC0abX1A0NaaUdzNzLkji7YqaQ9gWgckghEm3Y4q4AeXq506dTB1qE0KlcXR/r6ekh7AtEoJBGINktvMPHzqYsEtvLWxDcS5NeV42cLqawy2DoU0cpJIhBt1olfiqiqNra5+oFagf4aDEaFI6cLra8sxE1IIhBtVlpmPioVDL6jbSaCgb09sVerOCz1BOI2SSIQbdbhrAL6du+Em4ujrUNpEs5O9gT08pSGZeK21SsRJCYmMmnSJCZOnHjTcYMXLlzIli1bzNOpqalMmzaNqKgoYmJiyMnJAWDfvn2MGDGCqKgooqKieOmll27zNISwVFlt4PjZwlbf26g1QX5dOZlTTGl5ta1DEa2Y1USg0+lYvXo1mzZtIj4+nk8//ZSsrKw668ybN48dO3ZYzF+wYAHLly8nISGByMhIli9fDkBGRgYzZ84kISGBhIQEVq5c2YinJAQcOV2Iwai0mf6FbiTQX4OiXBmGU4hbYTURJCcnExISgoeHBy4uLoSGhpKUlGSxTmJiIuPGjSMsLMw8r7q6mvnz59O/f38AAgICuHDhAgDp6en88MMPREZGMm/ePPN8IRpLWmY+ajsVg/p0sXUoTapfz844OaolEYjbYnXM4ry8PDSaK4/XWq2WtLQ0i3VmzZoF1BQF1XJ0dCQqKgoAk8lEXFwc48ePB8DNzY2wsDAmTpzIv//9b2JjY/nkk08s9llSUkJJSYnFvNzc3Iacm2jHDmcVENCrM85O9RqWu9VysLdjUJ8u0p5A3BarvyUmk8mijxZFURrUZ0t1dTWLFi3CYDAwd+5cAJYtW2Ze/uijj/LWW29RWlqKm9uVQUM2bNhAXFxcvY8jRK3L5dWcyr7Eb8cH2DqUZhHo15UP/3uEopJKOrs72zoc0QpZLRry9vYmP//KWwn5+flotdp67bysrIxZs2ZhMBhYt24dDg4OmEwm1q1bh9FotFhXrVZbTMfExLBr1y6Lz80qqoWolXHqIiaFNtt+4Fq19SBp8lQgbpHVRDBq1ChSUlIoLCykoqKCnTt3Mnr06HrtfMGCBfTq1Ys1a9bg6FjzCp+dnR1fffWVuWI5Pj6eoKAgXFwsuwh2d3fH19fX4uPt7d3Q8xPt0OHMfBwd1AT06mzrUJpF3+4edHS2l0QgbpnVoiEvLy9iY2OJjo5Gr9czbdo0AgMDmT17Ns8++yxDhgy57nZHjhxh165d+Pn5MWXKFKCmfmH9+vW88cYb/OUvf2Ht2rV4enry5ptvNu5ZiXYtLauAQX08cbBXW1+5DVDbqRh8R1dpTyBuWb1q0iIjI4mMjLSYt379+jrrvf766+bvAwcO5Pjx49fdn7+/f53KYSEaQ1FJJb/kljJ2eA9bh9KsAv27svfnXHSF5W1mAB7RfKRlsWhTaotHAttYt9PW1DacS5enAnELJBGINiUtq4COzvbc4eth61CaVU9vNzq5OsprpOKWSCIQbcrhzHwG39EVtV3bGZayPlQqFYF+GtIyC1AUxdbhiFZGEoFoM3IvlqErLCfIv233L3QjgX5dKSypJCf/sq1DEa2MJALRZpjrB9pJ+4Fr1Z63dDchGkoSgWgz0jIL8HBzoqeXm/WV2yCfLh3p6tFB6glEg0kiEG2CoiikZeUT6Ne1QV2gtCU19QRdSc8qwGSSegJRf5IIRJtwTldKUWlVmx2fuL6C/LtSUlbN2dwS6ysL8StJBKJNqK0faC/9C93IkDtqEqF0NyEaQhKBaBMOZ+aj9XTBu0tHW4diU5rOHejWtSNpmZIIRP1JIhCtntGkkH7yIkHtrDXxjQT6a8g4VYDRaLJ1KKKVkEQgWr3TOcWUVegJbKftB64V6NeV8koDJ3OKbR2KaCUkEYhW73BmTf867a1/oRsZckfNdai9LkJYI4lAtHppWQX08HLDU0bnAsDDzYnePu5SYSzqTRKBaNX0BhM/n5b6gWsF+nXlyOlC9Aaj9ZVFuyeJQLRqJ34poqra2G67lbiRQL+uVOuNHD9bZOtQRCtQr0SQmJjIpEmTmDhx4k3HDV64cCFbtmwxT58/f54ZM2bw4IMP8uSTT1JWVgZASUkJc+bMISwsjBkzZliMiSxEQxzOzEelulIuLmoMuqMrdippTyDqx2oi0Ol0rF69mk2bNhEfH8+nn35KVlZWnXXmzZtnHoe41quvvspjjz1GUlISgwcP5t133wVgzZo1BAcHs337dqZPn86KFSsa8ZREe3LoRD5+vh64ujjaOpQWxbWDA3f4ekgiEPViNREkJycTEhKCh4cHLi4uhIaGkpSUZLFOYmIi48aNIywszDxPr9ezf/9+QkNDAW7PauwAACAASURBVJg6dap5u927d5uHvoyIiOC7775Dr9db7LOkpITs7GyLT25u7u2drWhTyiv1HP+liKH95LXR6wn068rxs4VUVhlsHYpo4ayOWZyXl4dGc+UXTavVkpaWZrHOrFmzAEhNTTXPKyoqwtXVFXv7mkNoNBp0Ol2dfdrb2+Pq6kphYSFeXl7m7Tds2EBcXNytnpdoB2o7VxvWT2vrUFqkQH8NX3yTxZEzhdwZINdI3JjVRGAymSx6c1QUpV69O15vvRttpygKdnaWDycxMTFMmTLFYl5ubi4zZsywemzRPhw6kY+To5r+vTvbOpQWaWBvT+zVKtIy8yURiJuymgi8vb05cOCAeTo/Px+t1voPlaenJ6WlpRiNRtRqtcV2Wq2WgoICvL29MRgMlJWV4eFhOcasu7s77u7uDT0f0Y4cysxnUN8uONirbR1Ki+TsZE9AL0+pJxBWWa0jGDVqFCkpKRQWFlJRUcHOnTsZPXq01R07ODgQHBzMtm3bAIiPjzdvN2bMGOLj4wHYtm0bwcHBODg43M55iHam4FIF2XmXGSrdStxUoF9XTmZforS82tahiBbMaiLw8vIiNjaW6OhoJk+eTEREBIGBgcyePZv09PSbbrt06VI2b97MpEmTOHDgAM899xwA8+fP59ChQ4SHh7Np0yZefvnlxjkb0W4cOlHzyrFUFN/csH5aTArSG6m4KatFQwCRkZHmt3xqrV+/vs56r7/+usV09+7d+de//lVnPQ8PD957772GxCmEhUMn8vFwrelKQdxYv54euDjbc/BEHvcEdbN1OKKFkpbFotUxmRQOZ+YT5K9pt8NS1pdabUeQv4afjuehKDJ8pbg+SQSi1TmbW8Kly1VSLFRPwwK05BdVkJN/2dahiBZKEoFodaR+oGGG/XqdDh6XrlzE9UkiEK3Oocx8fLWudPXoYOtQWgXvLh3x6dqRgyfybB2KaKEkEYhWRW8wknHyojwNNNCwfhrSswrQG2T4SlGXJALRqhw7U0S13ijtBxpoWICWymojx84W2joU0QJJIhCtysETedjZqRgiA9E0SKBfV+zsVBw8LsVDoi5JBKJVOXQin4CenXFxlpboDeHi7ED/Xp0lEYjrkkQgWo3S8mpOZl+S+oFbNCxAy8mcYoovV9k6FNHCSCIQrcbB43mYFLizv/SkeSuG9dOgKDWjuglxNUkEotVIPZaHm4sj/j2k2+lb4dejM64dHKQ9gahDEoFoFUwmhZ+O5TEsQIPaTrqVuBVqOxVB/TQcPCHdTQhLkghEq3Aqp5hLl6sY3t/L+srihob103KxuJJzulJbhyJaEEkEolVIPVYzzKmMtHV7arub+EmKh8RVJBGIViH1WB5+PTzwcHOydSitmtbTBV+tK6lHdbYORbQg9RqPIDExkXXr1mEwGIiJiakzbvDRo0dZsmQJZWVlBAcH8+qrr1JcXMzMmTPN65SWllJUVMTBgwfZt28fzzzzDN7e3gAMHDiQlStXNuJpibaktLya42cLmT6+n61DaRPuGuhN4vcnKa/US3sMAdQjEeh0OlavXs2WLVtwdHTkkUceYcSIEfj5+ZnXWbBgAcuXL2fo0KEsXryYzZs389hjj5GQkACAyWQiJiaG2NhYADIyMpg5cyZz585totMSbcmh4/mYFAiW+oFGcdcAL7buzuLQiXxGBcpgNaIeRUPJycmEhITg4eGBi4sLoaGhJCUlmZfn5ORQWVnJ0KFDAZg6darFcoAvvviCDh06mEc5S09P54cffiAyMpJ58+Zx4cKFxjwn0cYcOKbDzcUB/57y2mhjGNDHk47O9hyQ4iHxK6uJIC8vD43mSktOrVaLTqe74XKNRmOx3Gg08t577/HCCy+Y57m5ufH444+TmJjImDFjzE8KVyspKSE7O9vik5ub2/AzFK2ayaTw0/E8hvXTymujjcRebcewAC37j+owmeQ1UlGPoiGTyWQxHKCiKBbT1pZ///339O7dm4CAAPO8ZcuWmb8/+uijvPXWW5SWluLm5maev2HDBuLi4m7hlERbcjLnEpdKqxg+QIqFGtNdA7354fB5TuZckgZ6wnoi8Pb25sCBA+bp/Px8tFqtxfL8/CuvohUUFFgs//rrr5k0aZJ52mQy8Y9//IM5c+agVqvN86/+DhATE8OUKVMs5uXm5tapqBZt296MXOxUECyJoFEN769FpYL9R3SSCIT1oqFRo0aRkpJCYWEhFRUV7Ny5k9GjR5uXd+/eHScnJ1JTUwFISEiwWH7o0CGCg4OvHNDOjq+++oodO3YAEB8fT1BQEC4uLhbHdXd3x9fX1+JT+5aRaD/2/pzLgD5dcO/oaOtQ2pROrk4E9OzMfqknENQjEXh5eREbG0t0dDSTJ08mIiKCwMBAZs+eTXp6OgCrVq1i5cqVPPjgg5SXlxMdHW3e/ty5c3Vu4G+88QYfffQR4eHhfPHFFyxfvryRT0u0BbrCcs5cKCFksPwB0BSCB3qRde4SRSWVtg5F2Fi92hFERkaa3/iptX79evP3/v378/nnn19328OHD9eZ5+/vzyeffNKQOEU7tO/nmpcD7h4oiaAp3D3Qm4+3H+PAUR0TRvSydTjChqRlsWix9v2cSw8vV7ppXG0dSpvU28edrh4d2PuzvI3X3kkiEC3S5Qo96ScL5GmgCalUKkIGeXPweB6VVQZbhyNsSBKBaJF+OqbDaFIYMcjH1qG0aSMDfag2mPhJhrBs1yQRiBZp78+5dHJ1pF8vebWxKQ3q0wU3F0dS0qV1f3smiUC0OAajidSjOu4e6C2tiZuYWm3H3YO82H8kF73BZOtwhI1IIhAtTlpWAWWVBu4eJPUDzWHUkG6UVRpIP1lg61CEjUgiEC3OnsPn6eBkL4PQNJOh/TQ4O6r5UYqH2i1JBKJFMRhNpKRf4O6B3jg6qK1vIG6bo4Oa4f29+DHjgnRC105JIhAtSnpWAaXl1dwTJP3kN6eRQ3woKq3i+NkiW4cibEASgWhR9qSdp4OTmjv7S7FQcwoe4IW9WkVy+nlbhyJsQBKBaDGMvxYL3TXQGycpFmpWHTs4MLSflh8On5fioXZIEoFoMdJPFlBSVs29UixkE2OGdafgUgVHzxTaOhTRzCQRiBbjh8O1xUIy9oAtjBjsg6ODmu8OZts6FNHMJBGIFsFcLDRAioVspYOTPXcP9GJP2nmMRmlc1p5IIhAtQlpWTbGQvC1kW6OH+VJ8uZrDmdK4rD2RRCBahG9Sz9Gxg4MMSWljwQO0dHS251spHmpX6pUIEhMTmTRpEhMnTmTjxo11lh89epSpU6cSGhrKkiVLMBhqurTdunUr9957L1FRUURFRbF69WoASkpKmDNnDmFhYcyYMcNizGPR/lRUGUhOv8B9Q7tLIzIbc7BXM3JIN1LSL1ClN9o6HNFMrCYCnU7H6tWr2bRpE/Hx8Xz66adkZWVZrLNgwQJefvllduzYgaIobN68GYCMjAwWLVpEQkICCQkJxMbGArBmzRqCg4PZvn0706dPZ8WKFU1waqK1SEk/T1W1kbHDfW0digBGD+tORZWBAzKecbthNREkJycTEhKCh4cHLi4uhIaGkpSUZF6ek5NDZWUlQ4cOBWDq1Knm5enp6WzdupXIyEhefPFFiouLAdi9e7d56MuIiAi+++479Hp9o5+caB2+OZCNdxcXBvT2tHUoAgj064qHqxPf/iTFQ+2F1USQl5eHRqMxT2u1WnQ63Q2XazQa83KNRsNTTz3Fl19+iY+PD8uWLauzjb29Pa6urhQWWr67XFJSQnZ2tsUnN1eG1GtrCi5VcDgrnweG90Clki6nWwK12o4xd/qy/0guxZerbB2OaAZWB683mUwWv6CKolhM32z52rVrzfNnzZrFhAkTrnsMRVGws7PMSRs2bCAuLq6epyFaq90/ZaMocP/wHrYORVxlwoieJHx3km9SzzF5jJ+twxFNzOoTgbe3t0Vlbn5+Plqt9obLCwoK0Gq1lJaW8uGHH5rnK4qCWl1TEajVaikoqHk9zWAwUFZWhoeHh8VxY2Ji2LVrl8XnehXVovVSFIX/HTjHgN6e+HTtaOtwxFV6ebsT0LMzO/f+gqJIlxNtndVEMGrUKFJSUigsLKSiooKdO3cyevRo8/Lu3bvj5OREamoqAAkJCYwePRoXFxc++OADDh8+DMDHH39sfiIYM2YM8fHxAGzbto3g4GAcHBwsjuvu7o6vr6/Fx9tbBippS05mF3NOV8rYYHkaaIkmjOjJOV0pJ36RHknbOquJwMvLi9jYWKKjo5k8eTIREREEBgYye/Zs0tPTAVi1ahUrV67kwQcfpLy8nOjoaNRqNWvWrOGVV14hLCyMn3/+mQULFgAwf/58Dh06RHh4OJs2beLll19u2rMULdL2lDM4Oqi5b2h3W4ciruO+od1xclTz1b5fbB2KaGIqpRU992VnZzNu3Dh27dqFr6+8atialVXoiVm2g9FDu/Psw8NsHY64gTWf/ERy2gU+WhqKs5PVKkXRQlm7d0rLYmET36Seo6rayKRRfWwdiriJCXf3oqLKwA+HZZyCtkwSgWh2iqKwLfkMfj088OvhYX0DYTMD+3jSXdORnXvP2joU0YQkEYhmd+R0Ied0pUwa2dvWoQgrVCoVYaP6cPRMIVnnLtk6HNFEJBGIZrct+TQdne25b5hUErcG4+/qSQcnNV9+f9LWoYgmIolANKtLpVUkp53ngbt64uwolY+tQccODoy7qyffH8qhsKTS1uGIJiCJQDSr7SlnMBgVwqRYqFWJvLcvRpPC9uQztg5FNAFJBKLZVFYb+M8Pp7hroBc9vNxsHY5ogG4aV4IHeJGUcga9QbqnbmskEYhms2vfL5SUVfObsf62DkXcgofu68uly1V8dzDH1qGIRiaJQDQLo9HElm9P0r9XZwb2ke6mW6Mgfw09vd2I//ak9D/UxkgiEM1iT9p58grL+c0D/tLddCulUqn4zVg/zlwoYe/P0iV8WyKJQDQ5RVH44n9Z+GpduXugdBzYmo0Z5otPl478e+dxeSpoQyQRiCZ38Hg+p84XM/V+P+zs5GmgNVOr7fjteH9O5RSzX4aybDMkEYgmpSgK/9p+BE3nDtwvYxK3CfcP74GXp4s8FbQhkghEk0pOu0BWdjEzQvvjYK+2dTiiEdir7Zg+rh9Z5y6ReizP1uGIRiCJQDQZo9HEv7YfoYeXmwxF2cY8ENwDbecObNpxTJ4K2gBJBKLJfL3/HDn5ZURPGoBa6gbaFAd7Ox6dGEDmuUt8K+0KWr16JYLExEQmTZrExIkTrztu8NGjR5k6dSqhoaEsWbIEg8EAQGpqKtOmTSMqKoqYmBhycmp+YPbt28eIESOIiooiKiqKl156qRFPSbQEVXoj/955jIBenRkxSN4UaoseCO7JHb6d2PCfn6msNtg6HHEbrCYCnU7H6tWr2bRpE/Hx8Xz66adkZWVZrLNgwQJefvllduzYgaIobN682Tx/+fLlJCQkEBkZyfLlywHIyMhg5syZJCQkkJCQwMqVK5vg1IQtffndSS4WVxITPlDaDbRRdnYqZkcNoaC4kq27pWfS1sxqIkhOTiYkJAQPDw9cXFwIDQ0lKSnJvDwnJ4fKykqGDh0KwNSpU0lKSqK6upr58+fTv39/AAICArhw4QIA6enp/PDDD0RGRjJv3jzzfNE25F4s45OvTjByiA9D7uhq63BEExrUtwv3BHXji28yKbhUYetwxC2ymgjy8vLQaDTmaa1Wi06nu+FyjUaDTqfD0dGRqKgoAEwmE3FxcYwfPx4ANzc3Hn/8cRITExkzZgyxsbF1jltSUkJ2drbFJzdXWjO2dIqi8I+t6ajtYM7kIbYORzSD34cPxGRS2PDfI7YORdwiqx3Cm0wmi0d7RVEspq0tr66uZtGiRRgMBubOnQvAsmXLzMsfffRR3nrrLUpLS3Fzu9Ij5YYNG4iLi7vF0xK2kpJ+gQNHdTzx0GC6enSwdTiiGXh36ciU+/3Y/PUJxg7vwZ39tbYOSTSQ1ScCb29v8vPzzdP5+flotdobLi8oKDAvLysrY9asWRgMBtatW4eDgwMmk4l169ZhNFp2ZatWW75jHhMTw65duyw+16uoFi1HeaWe9+PT6dPNnch7ZVD69uTh8f3o4eXKO5sPUlaht3U4ooGsJoJRo0aRkpJCYWEhFRUV7Ny5k9GjR5uXd+/eHScnJ1JTUwFISEgwL1+wYAG9evVizZo1ODo61hzQzo6vvvqKHTt2ABAfH09QUBAuLi4Wx3V3d8fX19fi4+0tb5+0ZB/+5wiFJZU8PS0ItVreTG5PHB3UPPfInRSWVPJ/X2bYOhzRQFaLhry8vIiNjSU6Ohq9Xs+0adMIDAxk9uzZPPvsswwZMoRVq1bx5z//mcuXLzNo0CCio6M5cuQIu3btws/PjylTpgA19Qvr16/njTfe4C9/+Qtr167F09OTN998s8lPVDStlPTzbE85w5T7/QjoJd1Mt0f9enZmyv1+fPFNFvcEdWN4fy9bhyTqSaW0omaB2dnZjBs3jl27duHrK/3WtBT5RRU8+9Y3eHdx4c1nRuNgL08D7VW13shzq7+lvFLP356/n06uTrYOSWD93im/seK2GE0Kb21KxWgyseB3wZIE2jlHBzXPP3YnJWXVvPmvAxiNJluHJOpBfmvFbdm04xg/n7rIvKlBdNO42joc0QL4+Xrw1G+CSMsq4KNtR20djqgHSQTiln297xc2f32CiSN68UCwdConrhh/d0/CRvVmy+4sfjgsfRG1dJIIxC05nJlP3GeHGOqv4cnfBNo6HNECzY4aQv9enVnzyUGOnS20dTjiJiQRiAb7JbeElR/uo7vWlUUxd2Evr4qK63Cwt2Px7+/G082ZV9b/yOnzxbYOSdyA/AaLBjl7oYQl7yXj6KBm6RMhdOzgYOuQRAvW2d2Z1+aNooOjmr/8I5nsvFJbhySuQxKBqLes7Eu89O4e7FQqVjx5D1pPF+sbiXbPy9OF1+aNAuDP7yXzS26JjSMS15JEIOrl6OlC/rxuDx2c1Lz+9L308HKzvpEQv/LVuvHa3FEYTQoL434gPavA1iGJq0giEFbt+PEMi9ftwd3ViZVP34tP1462Dkm0Qn26dWLVs6PxdHfi5feT+Sb1nK1DEr+SRCBuqFpv5J3Nh4j77DCBfl15a/5otJ2lOEjcOi9PF978430M6N2Ftzf9xHtb0qjSG61vKJqU1b6GRPt04pci3tl8iDMXSvjt+H48Ftpfxh0WjcLVxZFX54Sw4b9HSfjuJGlZBSz43XD6dOtk69DaLUkEwkJllYGPk46R+P1JPNyc+MsTI7h7oPT6KhqXg72aWVGDubO/ljX//onn13zH5DF3MH2cPy7O8iZac5NEIADQG4zs3FvTUriwpJKwkb2JCR8or4eKJnVngJZ3XhzL/32Zwef/y+Tr/b8QHTaAB4J7SFfmzUgSQTtXUWVgd+o5PvtfJvlFFQzo7cnCx4MZ1LeLrUMT7UQnVyeef2w4Eff2ZX18On/ffIhPvz7B5DF3MP6unjg7yW2qqckVbocUReFkTjE7955ld2o2FVUG/Ht48MdpQxkWoLEYalSI5tKvZ2fefOY+fszIZcs3mfxjazqbdhxjzJ2+jB3eA/8eHvKz2UQkEbQTeoOR42eL2PtzLinpF9AVluNgb8d9Q7sTNrI3Ab06yy+ZsDmVSsXIIT6MHOLD0dOFJHx/kh0/nuU/P5ymu6YjIYN9GBagZWAfTxzs1dZ3KOqlXokgMTGRdevWYTAYiImJYcaMGRbLjx49ypIlSygrKyM4OJhXX30Ve3t7zp8/z4IFC7h48SJ9+vRh1apVdOzYkZKSEl588UXOnTuHp6cna9asQaPRNMkJtkeKopBXVMGpnGJO5lziyKlCjp8tpNpgwl5tx9B+Gn47vh8jh/jg5uJo63CFuK4BfTwZ0MeTyxV6ktPO8+1P2SR8d5IvvsnC2VFNQK/O9OvZmf69POnt405Xjw7YyZttt8TqCGU6nY5HH32ULVu24OjoyCOPPMLbb7+Nn5+feZ2IiAiWL1/O0KFDWbx4MYMHD+axxx5j7ty5PPTQQ4SHh7N27VrKy8tZsGABy5Ytw9vbmzlz5hAfH8/u3btZs2aN1WBlhLIaVXojxaVVXLpc87l4qYLci+XkFpbV/P9iGeWVBgDsVNCneycG9+3KoL5dCPLvKm9liFarvFJPelYBB0/kc+xsIafPl2Ay1dzCHB3UdNd0pLvGle4aVzw7OePpfuXTydWx3T5FWLt3Wn0iSE5OJiQkBA8PDwBCQ0NJSkrij3/8IwA5OTlUVlYydOhQAKZOncrf//53pk+fzv79+1m7dq15/u9+9zsWLFjA7t272bhxI1CTRJYtW4Zer8fB4coNqqSkhJISyz5JcnNzb+UaADV/JWecvMil0qqaaRQUBZQrK6DU/K92Rs3ya6ZrvtXOV2o3rfn26wrm5ddMK7+ubzKB0WjCYDShN5owGEwYTQoGw6/TRhN6g4mKKgMVVQYqf/1/RZWB8koDldV1G+A42Nvh5emCd5eODOztSU8fd/p2c6eXjzvOjlICKNoGF2cHRgz2YcRgHwAqqw2cyinmnK6U7LzLZOdd5mR2Mclp5zFd509ce7UdHTvY09HZAZcODnR0tsfZ0R4HezscHdQ42NvhoLbDofa7vR1qOxUqlQo7lQo7u5riK5UK1CoVKvMysFP9+r12nWsPflXR67XLri6VrbOl6so6Qf6aJnmKt3qHyMvLsyi20Wq1pKWl3XC5RqNBp9NRVFSEq6sr9vb2FvOv3cbe3h5XV1cKCwvx8roy2PWGDRuIi4u7zdO74tLlKv78j2TzXw8tib3aDgd7FfZqO9Rqu1+n7ejgaE8HZ3s83Jzx6WpPB6eaTydXRzxcnejk5oSHq5P5Lx55LBbtjbOjPQP7dGFgH8u33IxGE5cuV1FUUkVhSSUXSyopLaumvFJPWaWB8go9ZZV6yir0FF+uRm8woTcYf/2/iWqDCYPBeN1kYkvTx/kTPWlgo+/XaiIwmUwWlYiKolhM32j5tesBN6yMVBQFOzvLd4ZjYmKYMmWKxbzc3Nw69RP11dnNmX/+eQJlFXqLOFSqK3Gpfv1PbUa2yNK1Gb42O6P6ddvrrHPVfuos//V49moVDmo77H79i0II0XjUaju6dOpAl04dbms/RqMJk6JgNNWWECiYFDCZlF+/18w3ma58VxSlzh+cV09dWxp/s8L5a9ftrm2azh6tJgJvb28OHDhgns7Pz0er1Vosz8/PN08XFBSg1Wrx9PSktLQUo9GIWq222E6r1VJQUIC3tzcGg4GysjJz0VMtd3d33N3db/sEr9YYPxhCiPZDrbZDDbT1WjWrTfdGjRpFSkoKhYWFVFRUsHPnTkaPHm1e3r17d5ycnEhNTQUgISGB0aNH4+DgQHBwMNu2bQMgPj7evN2YMWOIj48HYNu2bQQHB1vUDwghhGg+VhOBl5cXsbGxREdHM3nyZCIiIggMDGT27Nmkp6cDsGrVKlauXMmDDz5IeXk50dHRACxdupTNmzczadIkDhw4wHPPPQfA/PnzOXToEOHh4WzatImXX365CU9RCCHEzVh9fbQlkddHhRCi4azdO6VXJyGEaOckEQghRDsniUAIIdq5VtXk1GisaVF7Oy2MhRCivam9Z9beQ6/VqhJBbXuFW21UJoQQ7Vl+fj69evWqM79VvTVUWVlJRkYGGo0GtbrhnUfVtkzeuHEj3t4tZ/hFiathJK6Ga6mxSVwNc6txGY1G8vPzGTx4MM7OznWWt6onAmdnZ4KDg297P97e3i3y9VOJq2EkroZrqbFJXA1zK3Fd70mgllQWCyFEOyeJQAgh2jlJBEII0c6pX3nllVdsHURzcnJyYsSIETg5Odk6FAsSV8NIXA3XUmOTuBqmKeJqVW8NCSGEaHxSNCSEEO2cJAIhhGjn2nQi2Lp1K/feey9RUVFERUWxevXqOutUV1ezYMECwsLCmDJlCidPnmyW2FJTU5k2bRpRUVHExMSQk5NTZ52cnByGDRtmjv+JJ55osngSExOZNGkSEydOZOPGjXWWHz16lKlTpxIaGsqSJUswGAxNFsvV4uLiCA8PJzw8nDfffPO6y8eOHWu+RteLvSk8/vjjhIeHm497+PBhi+W2ul6fffaZOaaoqCiGDx/OsmXLLNZpzmt2+fJlIiIiyM7OBiA5OZnIyEgmTpx43d9HgPPnzzNjxgwefPBBnnzyScrKypoltk8//ZSIiAgiIyN56aWXqK6urrNNfe4pjR3XSy+9xMSJE83H/Oqrr+psc9vXTGnDli1bpiQmJt50nQ8++ED5y1/+oiiKouzbt0+ZPn16c4SmjB07Vjl69KiiKIry2WefKfPmzauzTlJSkjm2ppSbm6uMHTtWKSoqUsrKypTIyEglMzPTYp3w8HDl4MGDiqIoyksvvaRs3LixyePas2eP8vDDDytVVVVKdXW1Eh0drezcudNinblz5yo//fRTk8dyNZPJpNx7772KXq+/4Tq2uF7XOnHihDJhwgTl4sWLFvOb65odOnRIiYiIUAYNGqScO3dOqaioUMaMGaP88ssvil6vV2bOnKns3r27znZz5sxR/vOf/yiKoihxcXHKm2++2eSxnTp1SpkwYYJSWlqqmEwmZeHChcr/+3//r8529bmnNGZciqIoERERik6nu+l2t3vN2vQTQXp6Olu3biUyMpIXX3yR4uLiOuvs3r2bhx56CIC77rqLwsJCzp8/36RxVVdXM3/+fPr37w9AQEAAFy5cuG78J06cICoqiujoaI4fP94k8SQnJxMSEoKHhwcuLi6EhoaSlJRkXp6Tk0NlZSVDhw4FYOrUqRbLm4pGo2HRokU4Ojri4ODAHXfcUeffJiMjg3/84x9ERkaybNkyqqqqmjyuU6dOATBz5kweeughNsFHJAAABdtJREFUPv74Y4vltrpe13rllVeIjY3F09PTYn5zXbPNmzezdOlS81jlaWlp9OrVix49emBvb09kZGSd66LX69m/fz+hoaFA0127a2NzdHRk6dKluLq6olKp6Nev33XvA/W5pzRmXBUVFZw/f57FixcTGRnJ3//+d0wmk8U2jXHN2nQi0Gg0PPXUU3z55Zf4+PjUeUQGyMvLQ6PRWGzT1L2bOjo6EhUVBYDJZCIuLo7x48fXWc/JyYmHHnqIrVu38sQTT/D0009f93H1dl17DbRaLTqd7obLNRqNxfKm4u/vb76Znjlzhu3btzNmzBjz8rKyMgYMGMCCBQvYunUrJSUlvPvuu00eV0lJCSNHjmTt2rV8+OGHfPLJJ+zZs8e83FbX62rJyclUVlYSFhZmMb85r9mKFSssuoSx9nMGUFRUhKurK/b2Nb3fNNW1uza27t27c8899wBQWFjIxo0bGTduXJ3t6nNPacy4CgoKCAkJ4a9//SubN2/mwIEDfP755xbbNMY1a1V9Dd3I9u3bWblypcW8vn378uGHH5qnZ82axYQJE+psqygKKpXKYtrOrvHy481iq66uZtGiRRgMBubOnVtn22eeecb8fcyYMbz11lucOnXK/CTRWEwmU51rcPW0teVNLTMzk7lz57Jw4UJ69+5tnt+xY0fWr19vnp45cyaLFy8mNja2SeMZNmwYw4YNM09PmzaNb7/91nwjsfX1Avjkk0/4wx/+UGe+ra4Z1O+6XG9ec147nU7HrFmz+M1vfsOIESPqLF+7dq35+43uKY2pR48eFsd8/PHHiY+P57e//a15XmNcszbxRBAWFsZ3331n8XnnnXcsEoGiKNftsdTLy4u8vDzzdEFBgfmxrKli+/DDDykrK2PWrFkYDAbWrVuHg4NDnW3/9a9/UVRUZHEOtVm/MXl7e5u7+IaarmqvvgbXLm/sa3Qzqamp/P73v+eFF15gypQpFsvOnz9v8ddRU12fax04cICUlJQbHteW1wtqih7379/PAw88UGeZra4ZWP85A/D09KS0tNTcb/711mkqJ0+e5JFHHmHKlCk8/fTTdZaXlpbW657SmI4fP86OHTssjnntv1djXLM2kQiux8XFhQ8++MD8NsfHH3983ew9ZswYEhISgJpfcCcnJ7p169bk8S1YsIBevXqxZs0aHB0dr7vO/v37zb+0+/btw2Qy0bdv30aPZdT/b+f+XROHwzCAv4tY/Be6OLl0aAenDgUH449gkLo6SMwgOCgOpbiWdmgKOrvYQQNOrVJFxLkdShdRpFMRC3USWwJtkPa54TCceAc9aCp3eT+j30AeHuL3DTG4u0s3Nzc0nU7p9fWVOp0O7e3tmeubm5vkdDrp7u6OiIjq9frSulWenp4onU7T2dkZiaK4sr6xsUGqqtJ4PCYAVK1WLb9DI/q5IZyenpJhGKTrOl1cXCydd119Ldzf35Pb7SaXy7Wytq7OiIi2t7fp4eGBRqMRvb+/09XV1UovDoeDvF4vtVotIiK6vLz8lu50XadkMkmZTIZkWf7tMZ/dU74SADo5OaHn52eaz+dUq9VWzvklnf3VT8v/mNvbW0SjUQSDQaRSKby8vAAANE1DsVgEALy9veHg4ADhcBjRaBT9ft/yXIPBAB6PB+FwGJIkQZIkKIqykm0ymSCRSEAURezv75tvGVmh0WhAFEUIgoBSqQQAUBQFvV4PADAcDhGLxRAIBJDL5WAYhmVZFo6OjrCzs2N2JEkSNE1bytVut83ch4eH35ILAAqFAoLBIARBwPn5OYD197XQbDaRzWaXPltnZz6fz3wD5vr6GpFIBIIg4Pj4GB8fHwCAfD6PbrcLAHh8fEQ8HkcoFIIsy5jNZpZnK5fL2NraWrrWFt/DX7P9aU+xKhcAVCoVhEIh+P1+qKpqHvOVnfFfTDDGmM39t4+GGGOMfQ4PAsYYszkeBIwxZnM8CBhjzOZ4EDDGmM3xIGCMMZvjQcAYYzbHg4AxxmzuB0lQiIWtMXtlAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "'''PDF, scatter plot, and histogram.'''\n",
    "# Generate the data\n",
    "x = np.arange(-5,15,0.1)\n",
    "# Plot a normal distribution: \"Probability density functions\"\n",
    "myMean = 5\n",
    "mySD = 2\n",
    "y = stats.norm(myMean, mySD).pdf(x)\n",
    "plt.plot(x,y)\n",
    "plt.title('Shifted Normal Distribution')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Random numbers with a normal distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Histogram of normally distributed data')"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "numData = 500\n",
    "data = stats.norm.rvs(myMean, mySD, size = numData)\n",
    "plt.plot(data, '.')\n",
    "plt.title('Normally distributed data')\n",
    "plt.show()\n",
    "\n",
    "plt.hist(data)\n",
    "plt.title('Histogram of normally distributed data')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Multiple normal sample distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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JMy955iPLvNry7FyQbm5u0nq9TovFIh0dzfNm9m63S9fX1+ns7CydnJz02pc85ZmbPPORZV778uxckABgCBY1ABCCggRACAoSACEoSACEoCABEIKCBEAIChIAIShIAISgIAEQgoIEQAgKEgAhKEgAhKAgARCCggRACAoSACF0/gpzXzLlS7tyk2de8sxHlnnty7NzQVqv176G950cX2ssz3vyzEue+cgyr7Y8OxekxWLxfofL5bL/kWW0ffM2Hb94OgvZtv1jbTabtFqt3mfRR9Q8mzLLneOdWvIcM7PnlJznc3nJcnhDt+F9eXYuSHdDzeVymU5PT/sd3QC+/ObnJ9t++eGrQf5XjmF35DwfZzlUjndqyHPszJ5Tap5N53BKshzLGG24Lc9iFzW83u6mPgQAMuo8Qori5fFRqN4oAP0UMUIyGhqObGF+op73RYyQjIbyeL3dpZfHD+dum7JNSb5Qs6jnfREFiTwU9hiaOgZN23ioLSPZ/a2GfBQkGJmOwceJ2quPooZ8iriHBED9FCToKOoNYSjdpFN2TXObr7a79Fkh853MUw1TIxDRpAWpbS7d/DrA/JiyAyAEBQmAEBQkeKdpscKrngsYLICAw3kfErwzxD1N7zlqVtKbNUtXUtYKEjC6nCsVa/iEgiGV1ClSkICiWYZfD/eQKuXeBVAaI6RKlTRMB9rN6cN4FaTCjdkwzdVTklraa1Pn8qfvvxjt/4+Z42gFKVojqKXXMeb8ubl6SlJzex1zBmTMHEcrSNGmkKIdD9SoxE4e0zFlBwym5lEK+VllB0AWTat7u6z4ncUIybQB0dVyT5N563srZBYFyf0ioiu9jSqe5DCLglQLJz1RuVdEDgpSQUrqRdfyHhCgWTHvQ3LRQY8Z6jZEB3mQglRST57+dECGYZTJ3Jiyo7fIHZCSL+pGmfNSQpscmoIUkIaZj4t6XjW3zamfm7aaoSBN/SLWSMMcnnb7cWpum03PbfvXnxMdzTx1Lki73d/vut1sNu+3ff3drw/+5sdvP3/yQl5dXU2yrevjD3H33O+y6KMpz5SaT4ShnvNY/+tu+2ND59l0HH/8/lvWdtvlb3O8Ns+ZIs8umXzM9tz/o83jv9/+658ppWHP9ef+f0qxz+Wu19V9bfOT29vb28bftLi8vEyr1arLQ6p1cXGRzs/Pe+1DnvfkmZc885FlXm15di5INzc3ab1ep8VikY6O5jnlsdvt0vX1dTo7O0snJye99iVPeeYmz3xkmde+PDsXJAAYgk/7BiAEBQmAEBQkAEJQkAAIQUECIAQFCYAQFCQAQlCQAAhBQQIgBAUJgBD+H67o0FRTLHehAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 25 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The standard error of the mean, with 100 samples, is 0.193\n"
     ]
    }
   ],
   "source": [
    "'''Show multiple samples from the same distribution, and compare means.'''\n",
    "# Do this 25 times, and show the histograms\n",
    "numRows = 5\n",
    "numData = 100\n",
    "for ii in range(numRows):\n",
    "    for jj in range(numRows):\n",
    "        data = stats.norm.rvs(myMean, mySD, size=numData)\n",
    "        plt.subplot(numRows,numRows,numRows*ii+jj+1)\n",
    "        plt.hist(data)\n",
    "\n",
    "        plt.xticks([])\n",
    "        plt.yticks([])\n",
    "        plt.xlim(myMean-3*mySD, myMean+3*mySD)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "# Check out the mean of 1000 normally distributded samples\n",
    "numTrials = 1000;\n",
    "numData = 100\n",
    "myMeans = np.ones(numTrials)*np.nan\n",
    "for ii in range(numTrials):\n",
    "    data = stats.norm.rvs(myMean, mySD, size=numData)\n",
    "    myMeans[ii] = np.mean(data)\n",
    "print('The standard error of the mean, with {0} samples, is {1:5.3f}'.format(numData, np.std(myMeans, ddof=1)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Normality Check"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 4.,  4.,  4., 17., 21., 24., 11.,  9.,  2.,  4.]),\n",
       " array([-0.19978878,  0.82453251,  1.8488538 ,  2.87317509,  3.89749638,\n",
       "         4.92181767,  5.94613896,  6.97046024,  7.99478153,  9.01910282,\n",
       "        10.04342411]),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "'''Check if the distribution is normal.'''\n",
    "# Generate and show a distribution\n",
    "numData = 100\n",
    "data = stats.norm.rvs(myMean, mySD, size=numData)\n",
    "plt.hist(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Graphical test: if the data lie on a line, they are pretty much\n",
    "# normally distributed\n",
    "_ = stats.probplot(data, plot=plt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Data are probably normally distributed\n"
     ]
    }
   ],
   "source": [
    "# The scipy \"normaltest\" is based on D’Agostino and Pearson’s test that\n",
    "# combines skew and kurtosis to produce an omnibus test of normality.\n",
    "_, pVal = stats.normaltest(data)\n",
    "\n",
    "# Or you can check for normality with Kolmogorov-Smirnov test: but this is only advisable for large sample numbers!\n",
    "#_,pVal = stats.kstest((data-np.mean(data))/np.std(data,ddof=1), 'norm')\n",
    "\n",
    "if pVal > 0.05:\n",
    "    print('Data are probably normally distributed')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Values from the Cumulative Distribution Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "With a threshold of 2.00, you get 7.0% of the data\n",
      "To get 97.5% of the data, you need a threshold of 8.92.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "'''Calculate an empirical cumulative distribution function, compare it with the exact one, and\n",
    "find the exact point for a specific data value.'''\n",
    "\n",
    "# Generate normally distributed random data\n",
    "myMean = 5\n",
    "mySD = 2\n",
    "numData = 1000\n",
    "data = stats.norm.rvs(myMean, mySD, size=numData)\n",
    "\n",
    "# Calculate the cumulative distribution function, CDF\n",
    "numbins = 20\n",
    "counts, bin_edges = np.histogram(data, bins=numbins, density=True)\n",
    "cdf = np.cumsum(counts)\n",
    "cdf /= max(cdf)\n",
    "\n",
    "# compare with the exact CDF\n",
    "plt.plot(bin_edges[1:],cdf)\n",
    "plt.plot(x, stats.norm.cdf(x, myMean, mySD),'r')\n",
    "\n",
    "# Find out the value corresponding to the x-th percentile: the\n",
    "# \"cumulative distribution function\"\n",
    "value = 2\n",
    "myMean = 5\n",
    "mySD = 2\n",
    "cdf = stats.norm.cdf(value, myMean, mySD)\n",
    "print(('With a threshold of {0:4.2f}, you get {1}% of the data'.format(value, round(cdf*100))))\n",
    "\n",
    "# For the percentile corresponding to a certain value: \n",
    "# the \"inverse cumulative distribution function\" \n",
    "value = 0.025\n",
    "icdf = stats.norm.isf(value, myMean, mySD)\n",
    "print('To get {0}% of the data, you need a threshold of {1:4.2f}.'.format((1-value)*100, icdf))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
